Dynamics of Density-Dependent Closure Term in a Simple Plankton Model

Abstract

A three-component aquatic model, which consists of nutrient, phytoplankton and zooplankton has been investigated. To incorporate the effects of higher predation, the mortality of zooplankton is assumed to be density-dependent (sigmoidal form). The system has uniformly bounded and dissipative solutions in the non-negative octant. Some conditions on persistence of all three-species have been established. The parameter estimation technique ”Marquardt-Levenberg (M-L) algorithm” has been used to estimate the values of some parameters, specially for density-dependent mortality. The bifurcation analysis reveals that model has periodic solutions for some parameter range. The amplitude of short term oscillations is varying with nutrient input present in the system. It is consistent with the field observational results. The nutrient input in the system may be one of the reason for short-term oscillations observed in the sea water.